for other readers, If you have a variac with a killawatt or similar device, you can easily prove this to yourselves via experimentation. A variac can adjust VAC from zero to +110% typically, and you can watch the response of your devices and the power draw. Many modern SMPS have variable input ranging from 100VAC-230VAC and multifrequency capability. Try such devices and other plug in devices you have around [ CFL or incandescent lightbulbs, powertools etc.,] and see what happens.
agree with digsys. pretty much everything will go up, no matter inductive, resistive or capacitive.
OK, but that is wrong for exactly the reasons everyone else has explained. Also, almost no loads in a typical house are simple passive linear loads. Almost every home load except for incandescent lamps have feedback loops of some sort to regulate their power draw. Efficiency will change slightly, but it can go either up or down -- it depends entirely on the device.